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Inverse Function Theorem

  1. Oct 11, 2006 #1
    I'm trying to see near which points of R^3 I can solve for theta, phi, and rho in terms of x,y, and z. I know i need to find the determinant and see when it equals zero; however, I get the determinant to equal zero when sin(phi) = 0, and when tan(theta) = -cot(phi). The first is right, but i've checked my work many times and keep getting the last solution. I just calculated the determinant of the partial derivatives (dx/dtheta, dx / dphi, dx / drho...dy/dtheta, dy/dphi, dy/drho...dz/dtheta, dz/dphi, dz/drho). I've checked my work many times. Am I correct, or am I doing something wrong?
     
  2. jcsd
  3. Oct 11, 2006 #2

    StatusX

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    That doesn't look right. What is the equation you got for the determinant?
     
  4. Oct 11, 2006 #3
    p = rho
    a = phi
    b = theta

    p^2[cos(a)sin(a)(cosb)^3 + (sina)^2(sinb)^3 + cos(b)cos(a)sin(a)(sinb)^2 + sin(b)(sina)^2(sinb)^2].

    I differentiated with respect to rho in the first column, phi in the second column, and theta in the third.

    Thanks.
     
  5. Oct 11, 2006 #4

    StatusX

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    I get something different. All I can suggest is go back through it carefully.
     
  6. Oct 11, 2006 #5
    thanks statusx for your time..i appreciate it
     
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